Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 4x + 2$ and $ BC = 5x - 1$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {4x + 2} = {5x - 1}$ Solve for $x$ $ -x = -3$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 4({3}) + 2$ $ BC = 5({3}) - 1$ $ AB = 12 + 2$ $ BC = 15 - 1$ $ AB = 14$ $ BC = 14$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {14} + {14}$ $ AC = 28$